Quantum-heat fluctuation relations in $3$-level systems under projective measurements

Abstract

We study the statistics of energy fluctuations in a three-level quantum system subject to a sequence of projective quantum measurements. We check that, as expected, the quantum Jarzynski equality holds provided that the initial state is thermal. The latter condition is trivially satisfied for two-level systems, while this is generally no longer true for $N$-level systems, with $N>2$. Focusing on three-level systems, we discuss the occurrence of a unique energy scale factor ${\beta }_{\mathrm{eff}}$ that formally plays the role of an effective inverse temperature in the Jarzynski equality. To this aim, we introduce a suitable parametrization of the initial state in terms of a thermal and a non-thermal component. We determine the value of ${\beta }_{\mathrm{eff}}$ for a large number of measurements and study its dependence on the initial state. Our predictions could be checked experimentally in quantum optics.

12 Pages, 6 Figures. Contribution to the Special Issue "Many Body Quantum Chaos" in honour of Shmuel Fishman, published in the journal "Condensed Matter"

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• Energy fluctuation relations and repeated quantum measurements
• Observation of partial and infinite-temperature thermalization induced by repeated measurements on a quantum hardware
• Stochastic entropy production: Fluctuation relation and irreversibility mitigation in non-unital quantum dynamics